Going for It on Fourth Down

It's 4th down and goal from the 2-yard line in the first quarter. What would most coaches do? Easy, they'd kick the field goal, a virtually certain 3 points.

But a 4th and goal from the 2 is successful about 3 out of 7 times, assuring the same number of expected points, on average, as the field goal. Plus, if the attempt at a touchdown is unsuccessful the opponent is left with the ball on the 2 or even 1 yard line. And if the field goal is successful, the opponent returns a kickoff which leaves them usually around the 28-yard line. It should be obvious that on balance, going for the touchdown is the better decision.

That's the case made by economist David Romer, author of a 2005 paper called "Do Firms Maximize, Evidence from Professional Football." Romer's paper is an analysis of 4th down situations in the NFL. It is quite possibly the most definitive proof that coaches are too timid on 4th down. Romer's theory is that coaches don't try to maximize their team's chances of winning games as much as they maximize their job security.

Coaches know that if they follow conventional wisdom and kick--oh well, the players just didn't make it happen. But if they take a risk and lose, even if it is on balance the better decision, they'll be Monday morning quarterbacked to death. Or at least their job security will be put in question.

In case anyone doubts how much coaches are concerned about Monday morning criticism, just take their word for it. Down by 3 points very late in the 4th quarter against the winless and fatigued Dolphin defense, former Ravens coach Brian Billick chose to kick a field goal on 4th and goal from one foot from the end zone. The Dolphins went on to score a touchdown in overtime. Billick's explanation at his Monday press conference was, "Had we done that [gone for it] after what we had done to get down there and [not scored a touchdown], I can imagine what the critique would have been today about the play call." Billick, a nine-year veteran head coach and Super Bowl winner, was more concerned about criticism from Baltimore Sun columnists than the actual outcome of the game. He'd rather escape criticism than give his team the best chance to win.

Romer's paper considers data from 3 years of games. To avoid the complications of particular "end-game" scenarios with time expiring in the 2nd or 4th quarters, he considers only plays from the 1st quarter of games. So his recommendations should be considered a general baseline for the typical drive, and not a prescription for every situation.

Romer's bottom line is the graph below. The x-axis is field position, and the y-axis is the yards-to-go on 4th down. The solid line represents when it is advisable for a team to attempt the first down rather than kick. According to the analysis, it's almost always worth it to go for it with less than 4 yards to go. The recommendation peaks at 4th and 10 from an opponent's 33 yard-line.

Romer basically measures the expected value of the next score. Say it's 4th and 2 from the 35 yd line. He compares the value of attempting a field goal from the 35 with the point value of a 1st and 10 from the 33 (multiplied the probability of actually making the first down.) He also recognizes that a field goal isn't always worth 3 points, and a touchdown isn't always worth at least 6. The ensuing kickoff gives an expected point value to the opponent. There is a point value to having a 1st and 10 from one's own 25 yard line.

One weakness of the paper is that it dismisses the concept of risk as unimportant. Romer says that long-term point optimization should be the only goal, so coaches should always be risk neutral. But if the level of risk aversion were actually considered, we might find that coaches are more rational than he concludes.

But the paper makes a very strong case that coaches should go for it on 4th down far more often than they currently do. Job security for coaches seems to be the primary reason why they don't. At a meeting with some researchers making the case for more aggressive 4th down decision making, Bengals coach Marvin Lewis responded, "You guys might very well be right that we're calling something too conservative in that situation. But what you don’t understand is that if I make a call that's viewed to be controversial by the fans and by the owner, and I fail, I lose my job."

It would be great if a coach came along and rarely kicked. It would be gamble, but if Romer and others are right, chances are the coach would be successful. And the rest of the NFL would have to adapt. It might only take one brave coach.

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8 Responses to “Going for It on Fourth Down”

  1. Anonymous says:

    I love reading your blogs. Keep up the great work.

    Some time ago you wrote, that we might find out which was better, the straight ahead running back like Jamal Lewis or boom or bust running backs like Barry Sanders.
    Is that something you are working on?

  2. Anonymous says:

    Billick's decision was inexcusable. You don't even have to rely on Romer, because he did not have to go through the myriad of possibilities after the decision. The equation is simple--chances of scoring on one play from inside the 1, versus chances of winning in OT. The first one is roughly 70%, the second roughly 50%. Not even close. He wasn't the only one to do that, as I also watched Whisenhunt make the exact same decision at home against SF, and like Billick, his team lost to an inferior team in overtime, when they could have won the game outright against not particularly good front sevens.

    Brian, a couple of years ago, I also looked at coaches decisions on 4th and 3 or less situations for the 2005 season. I cannot find the file, so I can't report specifics. However, I do remember one general thing that stood out. I compared the coach's aggressiveness rating with the team's offensive/defensive balance. Thus, teams like Houston and Oakland 2005 were "offensive" teams because though their offenses weren't great, they were relatively better than their defenses. When I did that, and compared it to the coach's aggressiveness from their own 40 to the opponent's goal (teams universally rarely go for it inside their own 40), I found that for "offensive" or "balanced" teams, being too conservative (compared to the league average) or very conservative (for a balanced team) was very costly in terms of actual wins versus pythagorean wins. Coaches like Turner, Capers, and Haslett, as well as Vermeil, severely underperformed their pythag projections, and did not adequately match their aggressiveness with their team situation. Offensive teams that were aggressive in these situations, namely Belichek, but also guys like Shanahan and Fisher, were near or above their pythag projections.

    However, for defensively skewed teams, there was no correlation between aggressiveness/conservatism and pythag performance. Being conservative didn't cost these coaches, but being overly aggressive, for the overall group, did not either.

    I would be interested if you could try to duplicate a study on the last few seasons using your efficiency numbers, to see if being too conservative on an offensive team is particularly costly, while being overly aggressive on a defensive team is not. Such a finding would be further evidence in support of Romer.

  3. Brian Burke says:

    24-I'd like to do some work on that. But first I need a play-by-play database. In other words, I need the yards gained/lost on every carry, not just an average for a season or even a game. This off-season I'm working on a way to generate exactly that. But it is a large project.

    JKL-Interesting. I've found that coaches aggressiveness on 4th down correlates with losing, or more precisely, desperation. There are some exceptions, like Belichick and Del Rio this year. Otherwise, it's the teams that are frequently behind in the 4th quarter that get aggressive. It makes sense.

    It also fits in with the idea that the stronger a team's defense is, the more conservative its offense can be.

    Say your defense gives up 30 points every game, and your offense always scores 24. In a very simple world, you could go 0-16. You'd be better off gambling and scoring 34 sometimes and 10 points sometimes. Your total net points would be the same, but you have a chance of winning 5 or 6 games. The point is that over-matched teams should be aggressive from the first kickoff and not wait until the 4th quarter to increase their risk tolerance.

    I'd like to isolate the first 3 quarters and just look at those 4th down situations. This would tell us more about the coaches independent from end-of-game desperation. Again, a play-by-play database would make this possible.

  4. Anonymous says:

    I did actually limit the situations, but like I said, I can't find the file (probably deleted it). I think it was probably something like the first 3 quarters, and only if within 10 points either way. I did go through the play by play, but it was tedious and I dont want to do it again.

    I agree if you just look at raw 4th down rates, it will be overrepresented by bad teams.

  5. Anonymous says:

    Herm Edwards, coaching the Jets, did the same thing, down three. I think it was fourth and one or two. With the win or loss in his hands if he goes for it, he takes the field goal and goes for OT. Loss is out of his hands!

  6. Brian Burke says:

    JKL-I know what you mean by tedious. I would be great to have a pay-by-play database, like FO does, but one we could share openly and build on. Sort of a football version of baseball's Retrosheet. I'm working on something that might have some promise.

    Anon-I love Herm, but he's afflicted like all the other coaches out there.

    I think coaches are thinking of "how far they've come" too. Billick's quote is revealing on many levels. He displays a fan's perspective when he says,"after what we had done to get down there." It doesn't matter if you drove 99 yards with miraculous plays or if you lucked into a turnover. 4th and 1 on the goal line is 4th and 1 on the goal line. The only thing that should really matter is the probability of winning the game, not spoiling a nice narrative about the drive in question.

  7. Unknown says:

    Brian, I do not have a question specifically pertaining to this article, but wanted to get your attention here....
    I have sent you an email, but you have indicated that you monitor these posts more frequently, so I wanted to give you a heads up.


  8. Anonymous says:

    Love those charts man! What's your secret?

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